If I signed a contract with a firm citing under California law however company is not registered in CA, is contract valid in CA?

It depends what kind of contract it is. You should talk with a lawyer. It sounds like you are mixing up two things choice of law written into the contract, and whether a firm not registered in the state can do business in the state. If you mean the choice of law of the contract is for California law, usually that does not affect the validity of the contract, but simply states that if the contract goes to court, that the court will interpret the contract under the laws of California. The laws of a certain state may be chosen for any number of reasons, including that the work will take place in that state or that the state has a good body of law in that subject area. For example, many contracts in music will be written with the choice of law as California since California has a good body of well-developed law on the topic of music. However, if you are talking about some sort of contract for services where the company might be required to be registered or licensed in California, such as disaster recovery or building, then the contract may not be valid on that basis. That is why you need to show the contract to a lawyer.